# Effect of apperture diffraction and fourier plane

• taimoortalpur
In summary, the diffraction of a finite wave can be explained by the concept of an apperture and the wave's huygens principle. The Fourier transform emerges as the wavefront becomes smaller in size.
taimoortalpur
Dear All,
I appreciate the efforts and support of members/admin here toward the goodness of education.

I am confusing a few concepts regarding diffraction, kindly help me out. I came up with following questions,

1. Is apperture required for diffraction or any finite wave will diffract?
To me considering finite wave will have somewhere an apperture, it should diffract.
2. If apperture is smaller than wavelenght do we get diffraction?
3. By huygens principle the wave diffract and must enlarge, how do we get Fourier transform (smaller in size usually for plane or spherical wave) in fresnel or franhofer plane.
4. Free space only add phase to propagation or also cause wave to diffract. (I think it do both)

Kindly also recommend any good book on diffraction that covers diffraction due to free space and Fourier imaging.

taimoortalpur said:
I am confusing a few concepts regarding diffraction, kindly help me out. I came up with following questions,

1. Is apperture required for diffraction or any finite wave will diffract?
To me considering finite wave will have somewhere an apperture, it should diffract.
2. If apperture is smaller than wavelenght do we get diffraction?
3. By huygens principle the wave diffract and must enlarge, how do we get Fourier transform (smaller in size usually for plane or spherical wave) in fresnel or franhofer plane.
4. Free space only add phase to propagation or also cause wave to diffract. (I think it do both)

Kindly also recommend any good book on diffraction that covers diffraction due to free space and Fourier imaging.

1) yes. And you are also correct, any finite wave is equivalent to an infinite wave that has passed through an aperture.

2) yes. There may not be propagating modes, tho. Look up "near-field scanning optical microscopy".

3) The Fourier transform emerges only in the Fraunhofer region: the far-field. This is because the diffracted wavefront can be approximated as a (spectrum of) expanding plane waves, and in the far-field limit, the diffraction integral reduces to the Fourier transform.

The standard textbook is Goodman "Introduction to Fourier Optics". As a primer, I also suggest Gaskill's "Linear Systems, Fourier transforms, and Optics", colloquially known as "Introduction to Goodman".

Many Thanks For the reply it cleared a lot of concepts...

## 1. What is aperture diffraction and how does it affect images?

Aperture diffraction is a phenomenon that occurs when light passes through a small opening, such as a camera lens or telescope. It causes the edges of the opening to act as secondary sources of light, resulting in a blurring or distortion of the image. This effect is most noticeable when the aperture is small and the light source is bright.

## 2. How does the Fourier plane play a role in aperture diffraction?

The Fourier plane is a mathematical concept used to describe the distribution of light waves after passing through an aperture. In the context of aperture diffraction, the Fourier plane helps us understand how the blurring or distortion of the image is created by the secondary sources of light. It can also be used to predict the intensity and pattern of the diffraction effect.

## 3. Can aperture diffraction be avoided or minimized?

Unfortunately, aperture diffraction is an inherent physical characteristic of light and cannot be completely avoided. However, it can be minimized by using larger apertures or by using a diffraction mask to block out the secondary sources of light. Additionally, post-processing techniques such as deconvolution can be used to reduce the effects of diffraction on images.

## 4. Does aperture diffraction affect all types of light waves?

Yes, aperture diffraction affects all types of light waves, including visible light, infrared, and ultraviolet. However, the extent of the diffraction effect may vary depending on the wavelength of the light and the size of the aperture.

## 5. How does the diffraction limit relate to aperture diffraction?

The diffraction limit is a theoretical concept that describes the smallest details that can be resolved by a lens or telescope. It is directly related to aperture diffraction as the diffraction limit is determined by the size of the aperture. This means that smaller apertures will have a larger diffraction limit, resulting in a lower resolution image.

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